Happy hour exists to bring punters in and get them drinking. Once they have sufficiently imbibed, the prices can go up again, but they only go up to the price they would be otherwise. I suggest this is unambitious.

Instead, you get customers in at happy hour, then quietly jack up the prices of the
drinks. Later on, people will be less inhibited and their judgement will be impaired. Also, if they're buying rounds they are less likely to notice because working out the exact price would be difficult anyway, and still harder due to sozzlement.

More precisely, this is how it works. Drinks obtained at exactly six pm are free. The prices then climb steadily, reaching mean price at nine pm and a maximum at midnight before dropping again over the next eighteen hours, meaning there is a second mean price at nine am. The tills determine the prices according to the time of day exactly. So, say a drink is free at six pm, one pound a dozen and four bob at nine pm and three pounds a dozen bob at midnight. It would have cost a new penny at one minute past six, tuppence at two minutes past, threepence at three minutes past and so forth. This is also scaled, so for example spirits would climb and drop in price faster.

Since the customers know the drinks are free at six, they will crowd into the bar and get as many as possible at that time, but as they are queueing by then and may even be trapped in the middle of a crowd in front of the bar, they are likely to be too embarrassed not to buy a drink, which will still be very cheap though not free by the time they get there. Later on, they will no longer care so much about the prices and buy drinks anyway. Alternatively, they may care a lot about the prices and not buy as much, thereby preventing binge drinking.

An added advantage is that this is a bit like a confusopoly. People would need to know the exact time of purchase to know if they're getting a good deal and will become steadily less able to work out if this is the case. To this end, the bar will also have a complicated price structure in any case, such as special offers which are multiplied according to time of day and start at something like forty-seven minutes and twenty-two seconds past the hour and finish at twenty-two minutes and forty-seven seconds past the next hour, or are only valid if bought at an odd number of seconds into the hour, but are still subject to the multiplication rule, or prices which vary according to non-differentiable continuous functions. There could even be alternating sad and happy seconds or milliseconds to punish people whose timepieces are not synchronised with GMT.

Prices should decline after midnight so the line drawn around the clock joins up neatly without any nasty kinks in it.

The price of coffee works in reverse, making it more expensive to boost your mental arithmetic than impair it.

You have no notion as to the extent some people will go to get a free drink, do you. There are people for whom the desire, nay passion, about getting something for nothing will pierce even the thickest veil of intoxication. When forced to choose between NSA procreative sex with an appealing partner and getting a drink for free, will stand in line for the free drink.

They would have to be able to predict the future to a remarkable degree to be sure of acquiring a drink for which they hadn't paid a penny. It would be feasible for them to achieve an extremely cheap one, but a completely free one would be highly improbable.